The Vela Pulsar

22 March, 2023

If you could see in X-rays, one of the brightest things you’d see in the night sky is the Vela pulsar. It was formed when a huge star’s core collapsed about 12,000 years ago.

The outer parts of the star shot off into space. Its core collapsed into a neutron star about twice the mass of our Sun—but just 20 kilometers in diameter! Today it’s spinning around 11.195 times every second. As it whips around, it spews out jets of charged particles moving at about 70% of the speed of light. These make X-rays and gamma rays.

The Chandra X-ray telescope made a closeup video of the Vela pulsar! It shows this jet is twisting around.

But the most interesting part of all this, to me, are the ‘glitches’ when the neutron star suddenly spins a bit faster. Let me tell you a bit about those.

First, I can’t resist showing you what happened to the star that exploded. It made this: the Vela Supernova Remnant. It’s so beautiful!

This photo was taken, not by a satellite in space, but by Harel Boren in the Kalahari Desert in Namibia!

Then, I can’t resist showing you a little movie of the Vela pulsar… slowed down:

This was made using the Fermi Gamma-Ray Space Telescope. The image frame is large: 30 degrees across. The background, which shows diffuse gamma-ray emission from the Milky Way, is shown about 15 times brighter than it actually is.

Then I can’t resist showing you a closeup photo of the Vela pulsar, taken in X-rays by the Chandra X-ray Observatory:

The bright dot in the middle is the neutron star itself, and you can see one of the jets poking out to the upper right, while the other is aimed toward us.

Now, about those glitches.

Since it’s putting out powerful jets, which carry angular momentum, we expect the Vela pulsar to slow down—and it does. But it does so in a funny way: every so often there’s a glitch where it speeds up for about 30 seconds! Then it returns to its speed before the glitch—gradually, in about 10 to 100 days.

What’s going on? A neutron star has 3 parts: the outer crust, inner crust, and core. The outer crust is a crystalline solid made of atoms squashed down to a ridiculous density: about 10¹¹ grams per cubic centimeter. But the inner crust contains neutron-rich nuclei floating in a superfluid made of neutrons!

Yes: while helium becomes superfluid and loses all viscosity due to quantum effects only when it’s really cold, highly compressed neutrons can be superfluid even at very high temperatures And the funny thing about a superfluid is that the curl of its flow is zero except along vortices which carry quantized angular momentum, coming in chunks of size ℏ.

Glitches must be caused by how the outer crust interacts with the inner crust. The outer crust slows down. The inner crust, being superfluid, does not. This can’t go on forever, since they rub against each other. So it seems that now and then a kind of crisis occurs: in a chain reaction, vast numbers of superfluid vortices suddenly transfer some angular momentum to the outer crust, speeding it up while reducing their angular momentum. It’s analogous to an avalanche.

So, we are seeing complicated quantum effects in a huge spinning star 1000 light years away!

Scorpius X-1

20 March, 2023

If you could see X-rays, maybe you’d see this.

Near the Galactic Center, the Fermi bubbles would glow bright… but the supernova remnant Vela, the neutron star Scorpius X-1 and a lot of activity in the constellation of Cygnus would stand out.

Scorpius X-1 was the first X-ray source in space to be found after the Sun. It was discovered by accident when a rocket launched to detect X-rays from the Moon went off course!

But why is it making so many X-rays?

Scorpius X-1 is a double star about 9,000 light-years away from us. It’s a blue-hot star orbiting a neutron star that’s three times as heavy. As gas gets stripped off from the lighter star and sucked into the neutron star, it first forms a spinning disk. As it spirals down into the neutron star, it releases a tremendous amount of energy.

This gas is near the ‘Eddington limit’, where the pressure of radiation pushing outward and the gravitational force pulling inward are in balance!

Scorpius X-1 puts out about 23000000000000000000000000000000 watts of power in X-rays! Yes, that’s 2.3 × 10³¹ watts. This is 60,000 times the X-ray power of our Sun.

Scorpius X-1 is considered a low-mass X-ray binary: the neutron star is roughly 1.4 solar masses, while the lighter star is only 0.42 solar masses. These stars were probably not born together: the binary may have been formed by a close encounter inside a globular cluster.

The lighter star orbits about once every 19 days.

Puzzle. Why is such a light star blue-hot, rather than a red dwarf?

I want to read more about Scorpius X-1 and similar X-ray binaries! Besides the Wikipedia article:

• Wikipedia, Scorpius X-1.

I’m finding technical papers like this:

• Danny Steeghs and Jorge Casares, The mass donor of Scorpius X-1 revealed, The Astrophysical Journal 568 (2002), 273.

which gets into details like “The insertion of the calcite slab in the light path results in the projection of two target beams on the detector.” But I’d like to read a synthesis of what we know, like an advanced textbook.

X-Ray Chimneys

18 March, 2023

First astronomers discovered enormous gamma-ray-emitting bubbles above and below the galactic plane—the ‘Fermi bubbles’ I wrote about last time.

Then they found ‘X-ray chimneys’ connecting these bubbles to the center of the Milky Way!

These X-ray chimneys are about 500 light-years tall. That’s huge, but tiny compared to the Fermi bubbles, which are 25,000 light years across. They may have been produced by the black hole at the center of the Galaxy. We’re not completely sure yet.

Here’s an X-ray image taken by the satellite XMM-Newton in 2019. It clearly shows the X-ray chimneys:

Sagittarius A* is the black hole at the center of our galaxy. It’s an obvious suspect for what created these chimneys!

Puzzle. What’s the white circle?

For more, try this:

• G. Ponti, F. Hofmann, E. Churazov, M. R. Morris, F. Haberl, K. Nandra, R. Terrier, M. Clavel and A. Goldwurm, The Galactic centre chimney, Nature 567 (2019), 347–350.

Abstract. Evidence has increasingly mounted in recent decades that outflows of matter and energy from the central parsecs of our Galaxy have shaped the observed structure of the Milky Way on a variety of larger scales. On scales of ~15 pc, the Galactic centre has bipolar lobes that can be seen in both X-rays and radio, indicating broadly collimated outflows from the centre, directed perpendicular to the Galactic plane. On far larger scales approaching the size of the Galaxy itself, gamma-ray observations have identified the so-called Fermi Bubble features, implying that our Galactic centre has, or has recently had, a period of active energy release leading to a production of relativistic particles that now populate huge cavities on both sides of the Galactic plane. The X-ray maps from the ROSAT all-sky survey show that the edges of these cavities close to the Galactic plane are bright in X-rays. At intermediate scales (~150 pc), radio astronomers have found the Galactic Centre Lobe, an apparent bubble of emission seen only at positive Galactic latitudes, but again indicative of energy injection from near the Galactic centre. Here we report the discovery of prominent X-ray structures on these intermediate (hundred-parsec) scales above and below the plane, which appear to connect the Galactic centre region to the Fermi bubbles. We propose that these newly-discovered structures, which we term the Galactic Centre Chimneys, constitute a channel through which energy and mass, injected by a quasi-continuous train of episodic events at the Galactic centre, are transported from the central parsecs to the base of the Fermi bubbles.

The Fermi Bubbles

16 March, 2023


How come nobody told me about the ‘Fermi bubbles’? If you could see gamma rays, you’d see enormous faint glowing bubbles extending above and below the plane of the Milky Way.

Even better, nobody is sure what produced them! I love a mystery like this.

The obvious suspect is the black hole at the center of our galaxy. Right now it’s too quiet to make these things. But maybe it shot out powerful jets earlier, as it swallowed some stars.

Another theory is that the Fermi bubbles were made by supernova explosions near the center of the Milky Way.

But active galactic nuclei—where the central black hole is eating a lot of stars—often have jets shooting out in both directions. So I’m hoping something like that made the Fermi bubbles. Computer models say jets lasting about 100,000 years about 2.6 million years ago could have done the job.

The Fermi bubbles were discovered in 2010 by the Fermi satellite: that’s how they got their name. I learned about them by reading this review article:

• Mark R. Morris, The Galactic black hole.

I recommend it! I get happy when I hear there are a lot of overlapping, complex, poorly understood processes going on in space. I get sad when pop media just say “Look! Our new telescope can see a lot of stars! I already knew there are a lot of stars. But the interesting stories tend to be written in a more technical way, like this:

Another cool thing: we may have detected some neutrinos emanating from the Fermi bubbles! These neutrinos have energies between 18 and 1,000 TeV. That’s energetic! Our best particle accelerator, the Large Hadron Collider, collides protons with an energy of about 14 TeV. This suggests that the Fermi bubbles contain a lot of very high-energy protons—so-called ‘cosmic rays’ — which occasionally collide and produce neutrinos.

• Paul Sutter, Something strange is happening in the Fermi bubbles,, September 4, 2019.

See also these:

• Rongmon Bordoloi, Andrew J. Fox, Felix J. Lockman, Bart P. Wakker, Edward B. Jenkins, Blair D. Savage, Svea Hernandez, Jason Tumlinson, Joss Bland-Hawthorn and Tae-Sun Kim, Mapping the nuclear outflow of the Milky Way: studying the kinematics and spatial extent of the Northern Fermi bubble, The Astrophysical Journal 834 (2017) 191.

• P. Predehl, R. A. Sunyaev, W. Becker, H. Brunner, R. Burenin, A. Bykov, A. Cherepashchuk, N. Chugai, E. Churazov, V. Doroshenko, N. Eismont, M. Freyberg, M. Gilfanov, F. Haberl, I. Khabibullin, R. Krivonos, C. Maitra, P. Medvedev, A. Merloni, K. Nandra, V. Nazarov, M. Pavlinsky, G. Ponti, J. S. Sanders, M. Sasaki, S. Sazonov, A. W. Strong, and J. Wilms, Detection of large-scale X-ray bubbles in the Milky Way halo.

Also try this, for something related but different:

• Jure Japelj, Astonishing radio view of the Milky Way’s Heart, Sky and Telescope, February 3, 2022.

Runaway Supermassive Black Hole

14 March, 2023

Many galaxies have a ‘supermassive black hole’ at their center. These range from hundreds of thousands to billions times the mass of our Sun.

I was surprised to read that astronomers have found evidence for a supermassive black hole shooting out of its host galaxy. They’ve seen a long thin feature—apparently a ‘wake’ of shocked gas and young stars—stretching 200,000 light years from the galaxy’s center and ending in a bright object that’s putting out 100 million times more power than our Sun. It

This is consistent with a supermassive black hole that was thrown out the galactic center at a speed of 1600 kilometers/second, which has been traveling for about 40 million years. This speed is faster than the galactic escape velocity!

But what could be muscular enough to throw a supermassive black hole around?

Only two possibilities are known.

One is another supermassive black hole. When two galaxies collide, their central black holes meet – and may start orbiting each other. If a third galaxy with its own supermassive black hole crashes in, one of the three black holes can get flung out.

That seems quite reasonable to me: galactic collisions are fairly common.

The other possibility is weirder.

When two black holes collide, they can emit gravitational radiation that’s beamed mainly in one direction… and this can give them a ‘kick’ in the opposite direction. I find this surprising in the first place. And it’s more surprising that this effect can be big enough to kick a black hole out of a galaxy! But that’s what some calculations say.

The picture above is from this paper:

• Pieter van Dokkum, Imad Pasha, Maria Luisa Buzzo, Stephanie LaMassa, Zili Shen, Michael A. Keim, Roberto Abraham, Charlie Conroy, Shany Danieli, Kaustav Mitra, Daisuke Nagai, Priyamvada Natarajan, Aaron J. Romanowsky, Grant Tremblay, C. Megan Urry and Frank C. van den Bosch, A candidate runaway supermassive black hole identified by shocks and star formation in its wake.

Abstract. The interaction of a runaway supermassive black hole (SMBH) with the circumgalactic medium (CGM) can lead to the formation of a wake of shocked gas and young stars behind it. Here we report the serendipitous discovery of an extremely narrow linear feature in HST/ACS images that may be an example of such a wake. The feature extends 62 kpc from the nucleus of a compact star-forming galaxy at z=0.964. Keck LRIS spectra show that the [OIII]/Hβ ratio varies from ~1 to ~10 along the feature, indicating a mixture of star formation and fast shocks. The feature terminates in a bright [OIII] knot with a luminosity of 1.9×1041 ergs/s. The stellar continuum colors vary along the feature, and are well-fit by a simple model that has a monotonically increasing age with distance from the tip. The line ratios, colors, and the overall morphology are consistent with an ejected SMBH moving through the CGM at high speed while triggering star formation. The best-fit time since ejection is ~39 Myr and the implied velocity is v~1600 km/s. The feature is not perfectly straight in the HST images, and we show that the amplitude of the observed spatial variations is consistent with the runaway SMBH interpretation. Opposite the primary wake is a fainter and shorter feature, marginally detected in [OIII] and the rest-frame far-ultraviolet. This feature may be shocked gas behind a binary SMBH that was ejected at the same time as the SMBH that produced the primary wake.

For more about the kick caused by gravitational waves, try this:

• Manuela Campanelli, Carlos O. Lousto, Yosef Zlochower and David Merritt, Maximum gravitational recoil, Phys. Rev. Lett. 98 (2007), 231102.

Sundial Puzzle

4 November, 2022

I’ve quit explaining math on Twitter and moved my activities of that sort to Mathstodon. This is a branch of Mastodon, a federated social network that is run by its own users—not by an unpredictable self-centered billionaire.

It feels a lot like the internet of the late 80’s or early 90’s, with people pitching in to build things they themselves use, not serving as cogs in the giant machine of surveillance capitalism. I invite you to join us!

I plan to write things there, polish them up a bit and put them here. An example is my post about modes. Today I had fun solving a puzzle about sundials. My goal was to use the minimum amount of math.

Colin Beveridge posed this puzzle:

“Suppose I planted a metre-long straight stick vertically in the ground and traced the locus of the end of its shadow. What shape would it make? Happy to assume a locally flat Earth if it makes things easier.”

Equivalently: what curve is traced out by the shadow of the tip of a sundial during one day, if the shadow lands on flat ground?

The answer is: a hyperbola—or in one very special case a straight line!

To see this, work in Earth-centered coordinates and treat the Sun as a point S moving in a circle over the course of a day. Treat the ground as a plane P. Sunlight traces out a line L going from S to the sundial’s tip T and hitting this plane P at some point X.

As S goes around in a circle, what curve does X trace out?

That’s the math question I’m solving.

To solve it, we need an obvious math fact: as a point S goes around a circle, the line going through S and any point T traces out a cone.

And another less obvious but very famous fact: when we intersect a cone with a plane P we get a curve called a ‘conic section’, which can be a circle, ellipse, parabola, hyperbola, or a line.

So, the only question is which of these curves we can actually get!

As the Sun sets, the shadow of our sundial gets arbitrarily long—so we can only get a circle or ellipse if the Sun never sets.

We only get a parabola if the Sun sets in the exact same place on the horizon that it rises—since the two ‘ends’ of a parabola go off to infinity in the same direction.

All these cases are a bit unusual. In most circumstances the curve we get will be a hyperbola or a straight line.

We get a straight line only when the Sun rises at one point on the horizon, is straight overhead at noon, and sets at the opposite point of the horizon. This would happen every day if you lived at the equator and the Earth’s axis wasn’t tilted. But in reality this situation is rare.

So, the shadow traced out by a sundial’s tip is usually a hyperbola!

You can play around with these hyperbola-shaped shadows here:

• Intellegenti Pauca, Hyperbola shadows, Geogebra.

There’s a lot more one can say about this: for example, what happens with the change of seasons? But I wanted to keep this simple!

Click on this picture for some details about a nice sundial that shows off its hyperbolae:

Rapid Variable B Subdwarf Stars

19 January, 2022

A subdwarf B star is a blue-hot star smaller than the Sun. A few of these crazy stars pulse in brightness as fast as every 90 seconds! Waves of ionizing iron pulse through their thin surface atmosphere.

What’s up with these weird stars?

Sometimes a red giant loses most of its outer hydrogen… nobody is sure why… leaving just a thin layer of hydrogen over its helium core. We get a star with at most 1/4 the diameter of the Sun, but really hot.

It’s the blue-hot heart of a red giant, stripped bare.

Iron and other metals in the star’s thin hydrogen atmosphere can lose and regain their outer electrons. When these electrons are gone, the metals are ‘ionized’ and they absorb more light. This pushes them further out. Then they cool, become less ionized, absorb less light, and fall back down. This heats them up, so they become more ionized and the cycle begins again.

This happens in standing waves, which follow spherical harmonic patterns. You may have seen spherical harmonics in chemistry, where they describe electron orbitals. The same math is being applied here to a whole star! Now it’s not the electron’s wavefunction that’s pulsing in a spherical harmonic: it’s metals in the atmosphere of a star.

When the star is rotating, spherical harmonics that would otherwise vibrate at the same frequency do so at different frequencies. So, just by looking at the pulsing of light from a distant subdwarf B star, you can learn how fast it’s rotating!

I got the gif of a pulsing star from here:

White Dwarf Research Corporation.

Pulsating white dwarf stars also oscillate in spherical harmonic patterns, and this website shows how they look.

The figure showing frequency lines is from this cool paper:

• Stephane Charpinet, Noemi Giammichele, Weikai Zong, Valérie Van Grootel, Pierre Brassard and Gilles Fontaine, Rotation in sdB stars as revealed by stellar oscillations, Open Astronomy 27 (2017), 112–119.

This paper says “a κ-mechanism triggered by an accumulation of heavy elements (in particular iron) in the stellar envelope caused by radiative levitation is driving the oscillation.”

So, what’s the κ-mechanism and radiative levitation?

The κ-mechanism causes oscillations when a layer of a star’s atmosphere gets more opaque at higher temperatures. For example, when heavy metals near the surface of the atmosphere get hot they can ionize, and thus absorb more radiation. When the layer of ions falls in it gets hotter, more opaque, blocks more escaping heat, and the star’s pressure goes up… pushing the layer out. But when the layer shoots out it gets cooler, less opaque, blocks less escaping heat, and the pressure drops again. So we can get oscillations!

Radiative levitation can drive heavy metals to the surface of a star. They absorb light, and the light literally pushes them up. This can make
these metals thousands of times more common than you’d expect near the surface.

There’s more that can happen with subdwarf B stars, and you can learn about it here:

• Wikipedia, Subdwarf B stars.

For example, they can simultaneously oscillate in two ways, at two separate rates!

Black Dwarf Supernovae

14 April, 2021

“Black dwarf supernovae”. They sound quite dramatic! And indeed, they may be the last really exciting events in the Universe.

It’s too early to be sure. There could be plenty of things about astrophysics we don’t understand yet—and intelligent life may throw up surprises even in the very far future. But there’s a nice scenario here:

• M. E. Caplan, Black dwarf supernova in the far future, Monthly Notices of the Royal Astronomical Society 497 (2020), 4357–4362.

First, let me set the stage. What happens in the short run: say, the first 1023 years or so?

For a while, galaxies will keep colliding. These collisions seem to destroy spiral galaxies: they fuse into bigger elliptical galaxies. We can already see this happening here and there—and our own Milky Way may have a near collision with Andromeda in only 3.85 billion years or so, well before the Sun becomes a red giant. If this happens, a bunch of new stars will be born from the shock waves due to colliding interstellar gas.

By 7 billion years we expect that Andromeda and the Milky Way will merge and form a large elliptical galaxy. Unfortunately, elliptical galaxies lack spiral arms, which seem to be a crucial part of the star formation process, so star formation may cease even before the raw materials run out.

Of course, no matter what happens, the birth of new stars must eventually cease, since there’s a limited amount of hydrogen, helium, and other stuff that can undergo fusion.

This means that all the stars will eventually burn out. The longest lived are the red dwarf stars, the smallest stars capable of supporting fusion today, with a mass about 0.08 times that of the Sun. These will run out of hydrogen about 10 trillion years from now, and not be able to burn heavier elements–so then they will slowly cool down.

(I’m deliberately ignoring what intelligent life may do. We can imagine civilizations that develop the ability to control stars, but it’s hard to predict what they’ll do so I’m leaving them out of this story.)

A star becomes a white dwarf—and eventually a black dwarf when it cools—if its core, made of highly compressed matter, has a mass less than 1.4 solar masses. In this case the core can be held up by the ‘electron degeneracy pressure’ caused by the Pauli exclusion principle, which works even at zero temperature. But if the core is heavier than this, it collapses! It becomes a neutron star if it’s between 1.4 and 2 solar masses, and a black hole if it’s more massive.

In about 100 trillion years, all normal star formation processes will have ceased, and the universe will have a population of stars consisting of about 55% white dwarfs, 45% brown dwarfs, and a smaller number of neutron stars and black holes. Star formation will continue at a very slow rate due to collisions between brown and/or white dwarfs.

The black holes will suck up some of the other stars they encounter. This is especially true for the big black holes at the galactic centers, which power radio galaxies if they swallow stars at a sufficiently rapid rate. But most of the stars, as well as interstellar gas and dust, will eventually be hurled into intergalactic space. This happens to a star whenever it accidentally reaches escape velocity through its random encounters with other stars. It’s a slow process, but computer simulations show that about 90% of the mass of the galaxies will eventually ‘boil off’ this way — while the rest becomes a big black hole.

How long will all this take? Well, the white dwarfs will cool to black dwarfs in about 100 quadrillion years, and the galaxies will boil away by about 10 quintillion years. Most planets will have already been knocked off their orbits by then, thanks to random disturbances which gradually take their toll over time. But any that are still orbiting stars will spiral in thanks to gravitational radiation in about 100 quintillion years.

I think the numbers are getting a bit silly. 100 quintillion is 1020, and let’s use scientific notation from now on.

Then what? Well, in about 1023 years the dead stars will actually boil off from the galactic clusters, not just the galaxies, so the clusters will disintegrate. At this point the cosmic background radiation will have cooled to about 10-13 Kelvin, and most things will be at about that temperature unless proton decay or some other such process keeps them warmer.

Okay: so now we have a bunch of isolated black holes, neutron stars, and black dwarfs together with lone planets, asteroids, rocks, dust grains, molecules and atoms of gas, photons and neutrinos, all very close to absolute zero.

I had a dream, which was not all a dream.
The bright sun was extinguishd, and the stars
Did wander darkling in the eternal space,
Rayless, and pathless, and the icy earth
Swung blind and blackening in the moonless air.

— Lord Byron

So what happens next?

We expect that black holes evaporate due to Hawking radiation: a solar-mass one should do so in 1067 years, and a really big one, comparable to the mass of a galaxy, should take about 1099 years. Small objects like planets and asteroids may eventually ‘sublimate’: that is, slowly dissipate by losing atoms due to random processes. I haven’t seen estimates on how long this will take. For larger objects, like neutron stars, this may take a very long time.

But I want to focus on stars lighter than 1.2 solar masses. As I mentioned, these will become white dwarfs held up by their electron degeneracy pressure, and by about 1017 years they will cool down to become very cold black dwarfs. Their cores will crystallize!

Then what? If a proton can decay into other particles, for example a positron and a neutral pion, black dwarfs may slowly shrink away to nothing due to this process, emitting particles as they fade away! Right now we know that the lifetime of the proton to decay via such processes is at least 1032 years. It could be much longer.

But suppose the proton is completely stable. Then what happens? In this scenario, a very slow process of nuclear fusion will slowly turn black dwarfs into iron! It’s called pycnonuclear fusion. The idea is that due to quantum tunneling, nuclei next to each other in the crystal lattice within a black dwarf will occasionally get ‘right on top of each other’ and fuse into heavier nucleus! Since iron-56 is the most stable nucleus, eventually iron will predominate.

Iron is more dense than lighter elements, so as this happens the black dwarf will shrink. It may eventually shrink down to being so dense that electron pressure will no longer hold it up. If this happens, the black dwarf will suddenly collapse, just like heavier stars. It will release a huge amount of energy and explode as gravitational potential energy gets converted into heat. This is a black dwarf supernova.

When will black dwarf supernovae first happen, assuming proton decay or some other unknown processes don’t destroy the black dwarfs first?

This is what Matt Caplan calculated:

We now consider the evolution of a white dwarf toward an iron black dwarf and the circumstances that result in collapse. Going beyond the simple order of magnitude estimates of Dyson (1979), we know pycnonuclear fusion rates are strongly dependent on density so they are greatest in the core of the black dwarf and slowest at the surface. Therefore, the internal structure of a black dwarf evolving toward collapse can be thought of as an astronomically slowly moving ‘burning’ front growing outward from the core toward the surface. This burning front grows outward much more slowly than any hydrodynamical or nuclear timescale, and the star remains at approximately zero temperature for this phase. Furthermore, in contrast to traditional thermonuclear stellar burning, the later reactions with higher Z parents take significantly longer due to the larger tunneling barriers for fusion.

Here “later reactions with higher Z parents” means fusion reactions involving heavier nuclei. The very last step, for example, is when two silicon nuclei fuse to form a nucleus of iron. In an ordinary star these later reactions happen much faster than those involving light nuclei, but for black dwarfs this pattern is reversed—and everything happens at ridiculously slow rate, at a temperature near absolute zero.

He estimates a black dwarf of 1.24 solar masses will collapse and go supernova after about 101600 years, when roughly half its mass has turned to iron.

Lighter ones will take much longer. A black dwarf of 1.16 solar masses could take 1032000 years to go supernova.

These black dwarf supernovae could be the last really energetic events in the Universe.

It’s downright scary to think how far apart these black dwarfs will be when they explode. As I mentioned, galaxies and clusters will have long since have boiled away, so every black dwarf will be completely alone in the depths of space. Distances between them will be doubling every 12 billion years according to the current standard model of cosmology, the ΛCDM model. But 12 billion years is peanuts compared to the time scales I’m talking about now!

So, by the time black dwarfs start to explode, the distances between these stars will be expanded by a factor of roughly

\displaystyle{ e^{10^{1000}} }

compared to their distances today. That’s a very rough estimate, but it means that each black dwarf supernova will be living in its own separate world.

The Expansion of the Universe

9 April, 2021

We can wait a while to explore the Universe, but we shouldn’t wait too long. If the Universe continues its accelerating expansion as predicted by the usual model of cosmology, it will eventually expand by a factor of 2 every 12 billion years. So if we wait too long, we can’t ever reach a distant galaxy.

In fact, after 150 billion years, all galaxies outside our Local Group will become completely inaccessible, in principle by any form of transportation not faster than light!

For an explanation, read this:

• Toby Ord, The edges of our Universe.

This is where I got the table.

150 billion years sounds like a long time, but the smallest stars powered by fusion—the red dwarf stars, which are very plentiful—are expected to last much longer: about 10 trillion years!  So, we can imagine a technologically advanced civilization that has managed to spread over the Local Group and live near red dwarf stars, which eventually regrets that it has waited too long to expand through more of the Universe.  

The Local Group is a collection of roughly 50 nearby galaxies containing about 2 trillion stars, so there’s certainly plenty to do here. It’s held together by gravity, so it won’t get stretched out by the expansion of the Universe—not, at least, until its stars slowly “boil off” due to some randomly picking up high speeds. But will happen much, much later: more than 10 quintillion years, that is, 1019 years.

For more, see this article of mine:

The end of the Universe.

Great Conjunction

5 December, 2020

I’ve been seeing Saturn and Jupiter coming closer to each other in the sky lately. Jupiter passes by Saturn every 19.6 years, and it’s called a great conjunction. But I just learned that on December 21st they’ll look closer than they have since March 1226! They’ll be just 0.1 degrees apart: 6.1 arcminutes, to be precise. That’s less than a fifth of the Moon’s apparent width.

Here’s the expected view from New York on December 16th, 45 minutes after sunset, when there will also be a crescent Moon:

Jupiter and Saturn were even closer on July 17, 1623—just 5.2 arcminutes apart—but the glare from the the Sun made them invisible from Earth. There will be another close great conjunction on March 15, 2080. Jupiter and Saturn will be just 6.0 arcminutes apart then! If you’re young, maybe you can see that one. Not me.

On February 16, 7541, Jupiter will actually pass in front of part of Saturn! This called a transit. But if you can wait that long, you might as well wait for June 17, 7541, when Jupiter will completely block the view of Saturn. This is called an occultation.

So yes, Jupiter passes by Saturn more than once that year! In fact it’ll do it three times: this is called a triple conjunction. Because the Earth moves around the Sun much faster than Jupiter or Saturn, these planets sometimes seem to move backwards in the sky, and thanks to this, there are some great conjunctions where Jupiter and Saturn come close to each other in the sky three times in rapid succession, like in 1682–1683:

I got this picture from here:

• Patrick Hartigan, Jupiter-Saturn conjunction series from 0 CE to 3000 CE.

You can have a lot of fun reading this. Since Jupiter and Saturn are in a 5:2 orbital resonance—that is, Jupiter orbits the Sun 5 times in the time it takes Saturn to go around twice—the great conjunctions are not random. Instead, they follow interesting patterns!

Puzzle. Why are triple conjunctions more common than double conjunctions?